Find-the-max-and-min-of-function-a-bsin-x-b-asin-x-where-b-gt-a-gt-0-in-the-interval-0-x-2pi-sketch-a-4-and-b-5-

Question Number 88040 by peter frank last updated on 08/Apr/20

F i n d t h e m a x a n d m i n

o f f u n c t i o n

\frac{a + b \sin x}{b + a \sin x}

w h e r e b > a > 0 i n t h e

i n t e r v a l 0 ⩽ x ⩽ 2 π . s k e t c h

a = 4 a n d b = 5

Commented by john santu last updated on 08/Apr/20

f (x) = \frac{bsin x + a}{asin x + b}

f^{'} (x) = \frac{(b^{2} - a^{2}) \cos x}{{(asin x + b)}^{2}} = 0

(b^{2} - a^{2}) \neq 0, then \cos x = 0

\cos x = 0 {\begin{cases} x_{1} = \frac{π}{2} \\ x_{2} = \frac{3 π}{2} \end{cases}

f (x_{1}) = \frac{b + a}{a + b} = 1 \leftarrow \max

f (x_{2}) = \frac{a - b}{b - a} = - 1 \leftarrow \min

Commented by peter frank last updated on 15/Apr/20

t h a n k y o u